ar X iv : m at h - ph / 0 20 70 25 v 2 1 4 N ov 2 00 2 Bound states due to a strong δ interaction supported by a curved surface

ar X iv : m at h - ph / 0 20 70 25 v 1 1 9 Ju l 2 00 2 Bound states due to a strong δ interaction supported by a curved surface

We study the Schrödinger operator −∆ − αδ(x − Γ) in L 2 (R 3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization, and is asymptotically planar in a suitable sense. We show that for a large enough α > 0 this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a " two-...

ar X iv : m at h - ph / 0 30 30 72 v 1 3 1 M ar 2 00 3 Eigenvalue asymptotics for the Schrödinger operator with a δ - interaction on a punctured surface

Given n ≥ 2, we put r = min{ i ∈ N; i > n/2 }. Let Σ be a compact, Cr-smooth surface in Rn which contains the origin. Let further {Sǫ}0≤ǫ<η be a family of measurable subsets of Σ such that supx∈Sǫ |x| = O(ǫ) as ǫ → 0. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator −∆−βδ(·−Σ\Sǫ) in L2(Rn), where β is a positive constant, as ǫ → 0. An analogous result is g...

ar X iv : m at h - ph / 0 20 30 28 v 1 1 8 M ar 2 00 2 Curvature - induced bound states for a δ interaction supported by a curve in R 3

We study the Laplacian in L 2 (R 3) perturbed on an infinite curve Γ by a δ interaction defined through boundary conditions which relate the corresponding generalized boundary values. We show that if Γ is smooth and not a straight line but it is asymptotically straight in a suitable sense, and if the interaction does not vary along the curve, the perturbed operator has at least one isolated eig...

ar X iv : n uc l - th / 0 41 10 95 v 1 2 3 N ov 2 00 4 Θ + pentaquark in the nuclear medium

We study the interaction of the Θ + pentaquark with nuclear matter associated to the KN decay channels and to the two meson cloud. We find that the potential is attractive and could be strong enough to lead to the existence of Θ + nuclear bound states.

ar X iv : m at h - ph / 0 31 10 01 v 4 3 N ov 2 00 4 Clifford Valued Differential Forms , Algebraic Spinor Fields